Modeling diseases with latency and nonlinear incidence rates: global dynamics of a multi-group model

2015 ◽  
Vol 39 (8) ◽  
pp. 1964-1976 ◽  
Author(s):  
Jinliang Wang ◽  
Xianning Liu
Keyword(s):  
Incidence Rates ◽  
Global Dynamics ◽  
Group Model ◽  
Nonlinear Incidence ◽  
Nonlinear Incidence Rates

scholarly journals Global dynamics of a delayed SIRS epidemic model with a wide class of nonlinear incidence rates

2011 ◽  
Vol 39 (1-2) ◽  
pp. 15-34 ◽  
Author(s):  
Yoichi Enatsu ◽  
Eleonora Messina ◽  
Yukihiko Nakata ◽  
Yoshiaki Muroya ◽  
Elvira Russo ◽  
...  
Keyword(s):  
Wide Class ◽  
Epidemic Model ◽  
Incidence Rates ◽  
Global Dynamics ◽  
Nonlinear Incidence ◽  
Sirs Epidemic Model ◽  
Nonlinear Incidence Rates

scholarly journals Stability Analysis of a Multigroup Epidemic Model with General Exposed Distribution and Nonlinear Incidence Rates

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Ling Zhang ◽  
Jingmei Pang ◽  
Jinliang Wang
Keyword(s):  
Death Rate ◽  
Sufficient Conditions ◽  
Incidence Rates ◽  
Global Dynamics ◽  
Lyapunov Functionals ◽  
Natural Death ◽  
Nonlinear Incidence ◽  
Nonlinear Incidence Rates ◽  
Basic Production ◽  
Derivatives Of

We investigate a class of multigroup epidemic models with general exposed distribution and nonlinear incidence rates. For a simpler case that assumes an identical natural death rate for all groups, and with a gamma distribution for exposed distribution is considered. Some sufficient conditions are obtained to ensure that the global dynamics are completely determined by the basic production numberR0. The proofs of the main results exploit the method of constructing Lyapunov functionals and a graph-theoretical technique in estimating the derivatives of Lyapunov functionals.

scholarly journals Analysis of Pine Wilt Disease Model with Nonlinear Incidence and Horizontal Transmission

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Muhammad Ozair
Keyword(s):  
Global Analysis ◽  
Horizontal Transmission ◽  
Disease Model ◽  
Pine Wilt Disease ◽  
Incidence Rates ◽  
Reproductive Number ◽  
Globally Asymptotically Stable ◽  
Nonlinear Incidence ◽  
Pine Wilt ◽  
Nonlinear Incidence Rates

The deterministic pine wilt model with vital dynamics to determine the equilibria and their stability by considering nonlinear incidence rates with horizontal transmission is analyzed. The complete global analysis for the equilibria of the model is discussed. The explicit formula for the reproductive number is obtained and it is shown that the “disease-free” equilibrium always exists and is globally asymptotically stable wheneverR0≤1. Furthermore, the disease persists at an “endemic” level when the reproductive number exceeds unity.

scholarly journals Asymptotic Behavior of Multigroup SEIR Model with Nonlinear Incidence Rates under Stochastic Perturbations

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Feng Wang ◽  
Shan Wang ◽  
Youhua Peng
Keyword(s):  
Asymptotic Behavior ◽  
Stochastic Perturbation ◽  
Incidence Rates ◽  
Nonlinear Incidence Rate ◽  
Stochastic Perturbations ◽  
Seir Model ◽  
Nonlinear Incidence ◽  
Nonlinear Incidence Rates ◽  
Uniqueness Of The Solution ◽  
Rate Functions

In this paper, the asymptotic behavior of a multigroup SEIR model with stochastic perturbations and nonlinear incidence rate functions is studied. First, the existence and uniqueness of the solution to the model we discuss are given. Then, the global asymptotical stability in probability of the model with R0<1 is established by constructing Lyapunov functions. Next, we prove that the disease can die out exponentially under certain stochastic perturbation while it is persistent in the deterministic case when R0>1. Finally, several examples and numerical simulations are provided to illustrate the dynamic behavior of the model and verify our analytical results.

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